L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonant asymptotics in an oscillating system with weak dissipation”, TMF, 160:1 (2009), 102–111; Theoret. and Math. Phys., 160:1 (2009), 960

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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 160, Number 1, Pages 102–111
DOI: https://doi.org/10.4213/tmf6382 (Mi tmf6382)

This article is cited in 16 scientific papers (total in 16 papers)

Autoresonant asymptotics in an oscillating system with weak dissipation

L. A. Kalyakin^a, M. A. Shamsutdinov^b

^a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
^b Bashkir State University

Full-text PDF (451 kB) Citations (16)

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DOI: https://doi.org/10.4213/tmf6382

Abstract: We study a system of two first-order differential equations arising in averaging nonlinear systems over fast single-frequency oscillations. We consider the situation where the original system contains weak dissipative terms. We construct the asymptotic form of a two-parameter solution with an unbounded increasing amplitude. This result gives a key for understanding autoresonance in weak dissipative systems as a phenomenon of significant increase in the forced nonlinear oscillation initiated by a small external pumping.

Keywords: nonlinear equation, perturbation, small parameter, asymptotic behavior, resonance, dissipation.

English version:
Theoretical and Mathematical Physics, 2009, Volume 160, Issue 1, Pages 960–967
DOI: https://doi.org/10.1007/s11232-009-0086-3

Bibliographic databases:

Language: Russian

Citation: L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonant asymptotics in an oscillating system with weak dissipation”, TMF, 160:1 (2009), 102–111; Theoret. and Math. Phys., 160:1 (2009), 960–967

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf6382

https://doi.org/10.4213/tmf6382

https://www.mathnet.ru/eng/tmf/v160/i1/p102

This publication is cited in the following 16 articles:

Sultanov O.A., “Autoresonance in Oscillating Systems With Combined Excitation and Weak Dissipation”, Physica D, 417 (2021), 132835
E. G. Ekomasov, V. N. Nazarov, K. Yu. Samsonov, R. R. Murtazin, “The possibility of controlling the dynamics and structure of a magnetic soliton in a three-layer ferromagnetic structure”, Tech. Phys. Lett., 47:7 (2021), 499–502
Ekomasov E.G. Nazarov V.N. Gumerov A.M. Samsonov K.Y. Murtazin R.R., “External Magnetic Field Control of the Magnetic Breather Parameters in a Three-Layer Ferromagnetic Structure”, Lett. Mater., 10:2 (2020), 141–146
Kalyakin L.A., “Capture and Keeping of a Resonance Near Equilibrium”, Russ. J. Math. Phys., 26:2 (2019), 152–167
Nazarov V.N., Ekomasov E.G., “Autoresonance Control Model of Nonlinear Dynamics of Magnetization in a Three-Layer Antiferromagnetic Structure in the Presence of Attenuation”, Lett. Mater., 8:2 (2018), 158–164
Kalyakin L.A., “Stability of the autoresonance in a dissipative system”, Russ. J. Math. Phys., 23:1 (2016), 77–87
O. A. Sultanov, “Random Perturbations of Autoresonance in Oscillating Systems with Small Dissipation”, J Math Sci, 219:2 (2016), 267
O. M. Kiselev, “Asymptotics of an autoresonance soliton”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 75–84
O. A. Sultanov, “Stability of autoresonance in dissipative systems”, Ufa Math. J., 7:1 (2015), 58–69
L. A. Kalyakin, “Lyapunov Functions in Justification Theorems for Asymptotics”, Math. Notes, 98:5 (2015), 752–764
L. A. Kalyakin, “Synchronization in a nonisochronous nonautonomous system”, Theoret. and Math. Phys., 181:2 (2014), 1339–1348
L. A. Kalyakin, O. A. Sultanov, M. A. Shamsutdinov, “Asymptotic analysis of a model of nuclear magnetic autoresonance”, Theoret. and Math. Phys., 167:3 (2011), 762–771
Kharisov A.T., Kalyakin L.A., Shamsutdinov M.A., “Autoresonance Excitation of Nonlinear Oscillations of Magnetization and Domain Walls in Ferromagnets”, Trends in Magnetism, Solid State Phenomena, 2011, 77–80
Shamsutdinov M.A., Kalyakin L.A., Sukhonosov A.L., Kharisov A.T., “Controlling quasi-relativistic dynamics of domain walls in the regime of self-phasing”, Physics of Metals and Metallography, 110:5 (2010), 430–441
A.T. Kharisov, L.A. Kalyakin, M.A. Shamsutdinov, “Autoresonance Excitation of Nonlinear Oscillations of Magnetization and Domain Walls in Ferromagnets”, SSP, 168-169 (2010), 77
L. A. Kalyakin, “Metod usredneniya v zadachakh ob asimptotike na beskonechnosti”, Ufimsk. matem. zhurn., 1:2 (2009), 29–52

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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